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University Physics with Modern Physics
CALC The motion of an underdamped oscillator is described by Eq. $(14.42) .$ Let the phase angle $\phi$ be zero. (a) According to this equation, what is the value of $x$ at $t=0$ ? (b) What are the magnitude and direction of the velocity at $t=0 ?$ What does the result tell you about the slope of the graph of $x$ versus $t$ near $t=0 ?$ Obtain an expression for the acceleration $a_{x}$ at
$t=0 .$ For what value or range of values of the damping constant $b$ (in terms of $k$ and $m )$ is the acceleration at $t=0$ negative, zero, and positive? Discuss each case in terms of the shape of the graph
of $x$ versus $t$ near $t=0$ .